Even K3,3's in Bipartite Graphs

We show that any internally 4-connected non-planar bipartite graph contains
a subdivision of K3,3 in which each subdivided path contains an even number
of vertices. In addition to being natural, this result has broader
applications in matching theory: for example, finding such a subdivision of
K3,3 is the first step in an algorithm for determining whether or not a
bipartite graph is Pfaffian. This is joint work with Robin Thomas.